"Divides Phi" category

[Batalov]

Originally Posted by sweety439

This is not "Divides Phi(695^94625,2)", i.e. k*b^n+1 does not divide Phi(b^n,2), and not belong to this category.

And wrong again.
You appear to look but not see. (Also explains your endless threads with miniature results.)

Look carefully at these first two lines (posted before) --

-----  -------------------------------- ------- ----- ---- --------------
 rank           description              digits  who year comment
-----  -------------------------------- ------- ----- ---- --------------
46623  2*3^152529+1                       72776    gb 2000     Divides Phi(3^152528,2)
88279  2*3^6225+1                          2971     C 1992     Divides Phi(3^6223,2)
94491  2*3^4217+1                          2013     C 1992     Divides Phi(3^4217,2)

[Dr Sardonicus]

I tried to find a precise description of the "divides phi" category, without success. The "Divides Phi" page here features

Definitions and Notes

Description to be added. Do you want to write it and supply the necessary references?

I note that the number k*(b^n) + 1 divides 2^(b^n) - 1, but divides the "primitive part" Phi((b^n)/m, 2) for a (very small) m. I also note that, with a composite b, m can be something other than a power of b.

As long as the divisor m is small enough (which it certainly is in the proffered examples), the fact that k*b^n + 1 divides Phi((b^n)/m,2) still proves that k*b^n + 1 is prime. So saying "it doesn't fit the category" is at best a minor quibble.

Perhaps some leeway could be included in the "Definitions and notes" part of the Divides Phi page, reflecting that the fact k*b^n + 1 "divides phi" also proves it prime.

[Stargate38]

@Batalov: Please tell me where to get DivPhi! I've been wanting to download it for over a month now.

[Batalov]

What could it be?
/scratches head/

[Stargate38]

Remove me form your ignore list right now! I want to use that program.

[sweety439]

Originally Posted by Batalov

And wrong again.
You appear to look but not see. (Also explains your endless threads with miniature results.)

Look carefully at these first two lines (posted before) --

-----  -------------------------------- ------- ----- ---- --------------
 rank           description              digits  who year comment
-----  -------------------------------- ------- ----- ---- --------------
46623  2*3^152529+1                       72776    gb 2000     Divides Phi(3^152528,2)
88279  2*3^6225+1                          2971     C 1992     Divides Phi(3^6223,2)
94491  2*3^4217+1                          2013     C 1992     Divides Phi(3^4217,2)

2*3^152529+1 is 6*3^152528+1 (with k=6, b=3), 2*3^6225+1 is 18*3^6223+1 (with k=18, b=3), thus they also divide Phi(b^n,2).

[Batalov]

The category is called "Divides Phi".
Not "Divides Phi(b^n,2)".

Originally Posted by https://primes.utm.edu/top20/page.php?id=37

These forms are defined in this collection's home page. This page is about one of those forms. Comments and suggestions requested. <-- so, follow that link. (Caldwell does not read this forum. No use writing a 'War and Peace' here)

It is an obvious extension (a superset) of the set of "Divides Fermat Number". Shares many of the same features in the structure of these rare factors.

This category also should have restrictions -- otherwise any prime "Divides Something".

[Batalov]

Originally Posted by Stargate38

Remove me form your ignore list right now! I want to use that program.

"...right now"!? Are you for real?
Isn't it self-explanatory using just this one post why you are on the ignore list?
And with posts like this you are not going to get off it, I can guarantee you that.

[Uncwilly]

Originally Posted by Stargate38

Remove me form your ignore list right now! I want to use that program.

That is awfully demanding. You want something from someone that has chosen to ignore you. If you are on their ignore list, why do you think that they would see your post? You catch more flies with honey....

[Stargate38]

Because I want to know where/how to download DivPhi. I've been waiting for weeks on end, with no download link or anything. Please give me a download link.

[Dr Sardonicus]

Originally Posted by Uncwilly

That is awfully demanding. You want something from someone that has chosen to ignore you. If you are on their ignore list, why do you think that they would see your post? You catch more flies with honey....

I'm pretty much at sea when it comes to computer terminology, but when I saw the original reference to the program in this thread

Originally Posted by Batalov

...and having the DivPhi self-compiled binary.

I did flag the modifier "self-compiled" as possibly important. Of course "binary" is important; I would hazard a guess that whether a precompiled binary actually works would depend very much on the system you try to run it on.

OK, enough of me proclaiming my ignorance for now...